In this chapter we present a review of some of the results we have obtained relating to the classical Hermite-Hadamard, Simpson and Milne Inequalities, through the use of weighted integral operators, illustrating their scope and generality. In general we use the notions of functions (h, m)-convex of first and second type, the classical Holder inequality, the power mean inequality, among others. Throughout the chapter, we point out that several of the results reported in the literature are, in fact, particular cases of those presented here.